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I recently watched this gif from this video, showing a magnet swinging towards a large disk of copper, where it stops gently before hitting the magnet. I understand that the eddy currents have a braking effect on the magnet. What I am curious about is how this would be affected if the copper disk was to be replaced by a superconductor.

Would it act similarly, or would it stop at a further distance from the superconductor than the copper (or not be stopped at all)? The closest thing that I could find was a discussion on whether a magnet would fall freely in a superconducting tube, which doesn't totally apply to this situation, and also wasn't totally clear.

I am only interested in the case of it swinging sideways, not being dropped from above.

For reference, the magnet starts in this position:Magnet on string held away from plate, before swinging sideways towards it

and ends in this position: Magnet on string hanging next to copper plate, after being slowed down by eddy currents

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  • $\begingroup$ Will the magnet induce eddy currents in the superconductor? $\endgroup$ – user207455 Apr 19 '19 at 5:41
  • $\begingroup$ @SolarMike I think that it would induce eddy currents (as it is a moving magnetic field near a conductor). I don't know how that would interact with the moving magnet, though. $\endgroup$ – fyrepenguin Apr 19 '19 at 5:52
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A great question! I cannot answer it in full detail, but one thing is certain.

The magnet will levitate over the superconductor's surface.

In the copper and magnet experiment, eddy currents in the copper disk dissipated due to resistance in the copper bulk. This is why the falling magnet is finally falling to the surface: the eddy current's magnetic field dies off as its energy is converted to heat.

The current in the superconductor does not die off, and keeps repelling the approaching magnet, stronger and stronger as it gets closer. At some point, the forces balance off.

Now, the picture is a little bit more complex that this. If you did not allow the falling magnet to rotate (make it fall always its north pole down), then the magnet would simply bounce off to its original height, and then continue bobbing up and down forever. But there is much more intricacy in a realistic experiment:

  • The approaching magnet's north pole is closer to the conducting surface, and feels stronger push back from the superconducting magnet (as soon as you started the eddy current, the superconducting piece is just a permanent magnet, assuming the current does not change). This fall is unstable, and a tiny deviation from the vertical will give an angular momentum to the falling magnet.
  • Assuming the surface the magnet falls to is not infinite, the magnet will also tend to slide sideways, as repelling magnets normally do if you try to push them together, because field lines won't be parallel to the finite superconducting surface.
  • In response, the superconducting magnetic field will adjust to counter any of these magnet movements. For example, both sideways and angular acceleration will receive a counter-push from the changing superconductor current.
  • The falling magnet is also a piece of metal, and subject to eddy currents from the magnet it falls onto, as long as its induced field varies. This is the chief source of damping the whole dynamics of the system. (There's of course air resistance, too.)
  • And there are two different types of semiconductors, which respond to the changes of external magnetic field differently: the induced field in one is smooth (perfectly smooth in theory), but the other's is rough and bumpy. These are called, somewhat uninventively, Type I and Type II, respectively.

In the experiment (oh, and can you imagine how much did we play with the first samples of high-temp superconducting YBaCuO ceramics we could only lay our grabby experimentalist hands on, when they were discovered in the late 80s!), the magnet tends to slide and escape the superconducting plate if you drop it roughly, but if you place it more carefully, it just stays there. If you push it, it slides but stops. If you give it a bit of rotation, the magnet will rotate, but then slow down and stop, too. It looks almost like it is suspended in a viscous liquid. Our first samples were so small that we only could play with a magnet on a string, which the tiny piece of superconductor promptly repelled. But over a sizable (a few centimeter in diameter), flat plate they were levitating steadily, if placed carefully enough.

This is how a high-temp, "bumpy field" type II superconductor behaves (I recall this is called “flux pinning”, but it's a bad name, IMO). However, I do not know from experience what would exactly happen if you dropped a magnet on a chunk of metallic type I superconductor as large as the experimenter's copper disk, as current (including out case of induced eddy current) in superconducting metals produces a very smooth magnetic field, and expel all magnetic field lines out of material. The high-temp ceramic, in contrast, lets some field lines through what you can think about as perfect quantum "holes" or thin tubes in the material. I think in this case the magnet would experience much less viscous interaction with its induced magnetic field, but would it eventually stabilize, or just end up sliding sideways forever (on until it finds the edge of the superconductor plate and falls, whichever comes first), and whether it will it stabilize rotationally or tumble, I do not know. All the above effects still apply, but I cannot clearly imagine the full dynamics. My best guess is that rotation and up/down bobbing would nearly (exponentially) cease due to induced eddy current losses the magnet, but there is nothing much I can think of to eat up the constant momentum of a magnet flying parallel to the semiconducting surface in the perfectly smooth field. I just do not know how "bumpy" is the field in real, not theoretically perfect superconducting metals.

EDIT: Here's a recorded experiment of this exact setup, with a bulk rare earth magnet levitating over a flat piece of superconducting ceramics: https://youtu.be/qYhnt6Q_dXg?t=205. The link is to the point in the video where the effect can be observed the best. The narration is physically irrelevant, to say the least, but the demonstration itself is very clear. The dark disk at the bottom of the liquid nitrogen bath is a piece of superconducting ceramic, and the shiny cube floating over it is a magnet.

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  • $\begingroup$ I think you may not have fully understood the situation that I am interested in. Specifically a magnet swinging sideways into the conducting plate. I added a couple of pictures to the question to help clarify, but the gif that I linked also shows that. I say this because I noticed you talk about the magnet "sliding off" and "levitating over" the superconductor, when that would not be likely to happen in this different setup. $\endgroup$ – fyrepenguin Apr 20 '19 at 2:25
  • $\begingroup$ @fyrepenguin, just apply essentially the same thinking. Ideally, the magnet will bounce elastically, without damping, forever. There is simply nothing there to dissipate energy inelastically. In the real world, the inelastic damper is the current induced in the magnet itself, as the magnet is also a chunk of metal; the bouncing will exponentially die (and slowly, you'll get quite a few). It won't be in-plane, the magnet will do the off-plane slide, and settle in an orbit (which may even be aperiodic, die to dumping). Your setup is simpler, think of it as a subset of a more general idea. $\endgroup$ – kkm Apr 20 '19 at 21:30
  • $\begingroup$ I think this answer would benefit from that being made clearer; the part in bold states that it would levitate above. I do think that you are right, that it will bounce repeatedly off of the magnetic field. I was mainly assuming that the motion would stay in-plane, and though I see how it could potentially slide sideways in this exact setup, I can definitely think of how to restrict its movement to a single plane. If you were to make that point clearer (that the magnet will elastically bounce until the current inside the magnet itself dampens it), I would feel comfortable accepting this. $\endgroup$ – fyrepenguin Apr 20 '19 at 23:25
  • $\begingroup$ @fyrepenguin, makes sense, thanks for the feedback. I'll make an update. Yep, I also think that things are quite simple as long as the movement is restricted to in-plane swinging. A less restricted dynamic system with damping may go chaotic quite easily, as a general case. Good math is scarce for this regime, so it's usually where it gets handwavy. But the exact dynamics is likely beyond the essence of the question, if I understand you. $\endgroup$ – kkm Apr 21 '19 at 1:02
  • $\begingroup$ @fyrepenguin, the more I search/think, the more confused I am. There are many accepted/upvoted answers that say e.g. the pendulum magnet in-plane along (not accross, as your is) an SC will experience perfect damping. I'd be skeptical, but I know from experience a levitating magnet does not like to move when pushed (I thought these were effects from finite size/edge, Type II flux-dotted field and magnet's own eddy-brake effect). I and some grad chatted on the weekend, but did not come to a conclusion! I'm on it, but I need more time for an update (I have only so much time for this, too :( ). $\endgroup$ – kkm Apr 23 '19 at 4:43

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